Corato G. 2, Moramarco T. 2, Tucciarelli T. 1 1 Department of Hydraulic Engineering and Environmental Applications, University of Palermo, Italy, Viale delle Scienze, 90128, Palermo, Italy 2 Research Institute for Geo-Hydrological Protection, CNR, Via Madonna Alta 126, Perugia, Italy

I. Hydrometric river site with rating curve known III. Equipped River reach with level observations only (Dyrac (Dottori et al., 2009), MAST (Aricò et al., 2009), VPMS (Perumal et al., 2007; 2010) Level observations Negligible lateral flows II. Hydrometric river site with unknown rating curve Jones Formula (Henderson, 1966), Fenton (Fenton, 1999), Marchi (1976) Level observations Stage (m) IV. Equipped river reach with rating curve known at one of ends (Rainfall-runoff modeling, Rating Curve Model) Rating Curve Level observations Significant lateral flows Four possible gauged station configurations for discharge monitoring

III. Equipped River reach with level observations only Level observations Negligible lateral flows In the context of the third configuration, the hydraulic DORA model (Tucciarelli et al. 2000), based on the diffusive hypothesis, can be applied. The model starting from observed stage hydrographs at channel ends, allows there of estimating discharge hydrographs by using a calibration procedure of Manning parameter based on the wave speed of the flood computed through observed stages (Aricò et al. 2009) However the model application, besides the need of topographical data of river sections, was found depending on the Manning’s roughness calibration procedure that affected the model performances

Purposes To address the minimum channel length, L, so that the effects of the downstream boundary condition on the computation of the upstream discharge hydrograph is negligible To propose a new procedure for Manning’s calibration also for a real-time context by exploiting instantaneous flow velocity measurements carried out by radar sensors and using the entropic velocity model

Using hydraulic modelling to optimize Configuration III Q x H x H n AR xTt H                         3/2 1 Diffusive form of Saint Venant Equation:

Boundary conditions or q(0,t) = q u (t) Flow driven Upstream h(0,t) = h u (t)Water level driven Downstream

Problem 1: Wath L? In Configuration III each possible downstream b.c. is an approximation of the physical one We need a reach long enough to avoid a strong estimation error of the discharge in the initial section It’s possible to get a rough estimation of the required length?

1.Large rectangular channel, with constant bed slope 2.Linear variation of water depth in the upstream section Hypothesis Numerical model Syntetic Test

Root hydraulic head gradient at upstream section: Qualitative behaviour

The previous problem can be solved numerically once for ever using dimensionless variables, for the most severe case of initially dry conditions Dimensionless model Dimensionless variables Dimensionless equations

The solution is function of L. The reference solution is computed for L= Error computation

2. from the previous graph, the corresponding value: L A priori estimation of L Relative Error 1. given E d, compute E from the above equation Procedure

In Configuration III the calibration of n is carried out using the stage hydrograph of the downstrem section We need a long enough reach to estimate the wave celerity In present method n can be estimated using a single mean velocity measurement Problem 2: Wath n?

Calibration Manning coefficent was determined minimizing the follow objective function: where q comp (t cal,n) is the computed discharge at the instant t cal in which measurement is carried out, while q obs is the observed discharge.

To develop a practical and simple method for estimating discharge during high floods, Moramarco et al. (JHE, 2004) derived from the entropy formulation proposed by Chiu an equation applicable to each sampled vertical: Entropic Method If the measurement is carried out in the upper part of the flow area, u maxv is sampled for each vertical. Anyway, to drastically reduce the sampling period it is possible to consider only the upper portion where u max typically occurs and assuming that the behaviour of the maximum velocity in the cross-sectional flow area can be represented through a parabolic or elliptical curve. Gauged site: M estimated through the recorded pairs of (u m, u max ) Problem 2: Estimatimation of calibration discharge

measuredellipticalparabolic Entropic Method Problem 2: Estimatimation of calibration discharge

Gauged Section: M.te Molino (Tiber River) – 28/11/05 ore 11:30 a) b) c) d)

Eventq pM [m 3 /s]t ph [h]h pM [m]Duration [h] December April November February December November Eventq pM [m 3 /s]t pq [h]h pM [m]Duration [h] November December Study Area: Upper Tiber Basin Pierantonio (1805 km 2 ) Ponte Nuovo (4135 km 2 )

Test case 1: Pierantonio Mean bed slope i = 1.6x10 -3 Typical Manning = sm -1/3 (observed during Nov. 05) L estimation

Test case 1: Pierantonio EventQ max Error [%] December April November February December November

Test case 1: Pierantonio Discharge Estimation Results Cal. Time [h] Man [sm -1/3 ] Q max err [%] Cal. Time [h] Man [sm -1/3 ] Q max err [%]

Test case 2: Ponte Nuovo Mean bed slope i = 0.85x10 -3 Typical Tiber Manning = sm -1/3 (observed during Nov. 05) L estimation

Test case 2: Ponte Nuovo Cal. Time [h] Man [sm -1/3 ] Q max err [%] Cal. Time [h] Man [sm -1/3 ] Q max err [%] Discharge Estimation Results

Conclusions The effect of downstream boundary condition over the upstream stage hydrograph computation has shown that short channel lengths are enough to achieve good performance of the diffusive hydraulic model The coupling of the hydraulic model with the entropic velocity model turned out of great support for an accurate calibration of Manning’s coefficient The developed algorithm can be conveniently adopted for the rating curve assessment at ungauged sites where the standard techniques for velocity measurements fail, in particular during high floods Based on the proposed procedure, discharge hydrographs can be assessed in real-time for whatever flood condition.